Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Saturday 30 May 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 125,165 x 9[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 female 0-18 e380000… nhs_bar… 35 rm13ae london
## [90m 2[39m 111 2020-03-18 female 0-18 e380000… nhs_bed… 27 mk454hr east_of_e…
## [90m 3[39m 111 2020-03-18 female 0-18 e380000… nhs_bla… 9 bb12fd north_west
## [90m 4[39m 111 2020-03-18 female 0-18 e380000… nhs_bro… 11 br33ql london
## [90m 5[39m 111 2020-03-18 female 0-18 e380000… nhs_can… 9 ws111jp midlands
## [90m 6[39m 111 2020-03-18 female 0-18 e380000… nhs_cit… 12 n15lz london
## [90m 7[39m 111 2020-03-18 female 0-18 e380000… nhs_enf… 7 en40dy london
## [90m 8[39m 111 2020-03-18 female 0-18 e380000… nhs_ham… 6 dl62uu north_eas…
## [90m 9[39m 111 2020-03-18 female 0-18 e380000… nhs_har… 24 ts232la north_eas…
## [90m10[39m 111 2020-03-18 female 0-18 e380000… nhs_kin… 6 kt11eu london
## [90m# … with 125,155 more rows[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 11
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 42
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 61
## 33 2020-04-02 East of England 64
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 92
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 91
## 43 2020-04-12 East of England 101
## 44 2020-04-13 East of England 77
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 63
## 50 2020-04-19 East of England 66
## 51 2020-04-20 East of England 66
## 52 2020-04-21 East of England 74
## 53 2020-04-22 East of England 66
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 65
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 44
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 35
## 67 2020-05-06 East of England 28
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 30
## 70 2020-05-09 East of England 26
## 71 2020-05-10 East of England 21
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 25
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 23
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 25
## 82 2020-05-21 East of England 20
## 83 2020-05-22 East of England 13
## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 16
## 86 2020-05-25 East of England 18
## 87 2020-05-26 East of England 12
## 88 2020-05-27 East of England 10
## 89 2020-05-28 East of England 6
## 90 2020-03-01 London 0
## 91 2020-03-02 London 0
## 92 2020-03-03 London 0
## 93 2020-03-04 London 0
## 94 2020-03-05 London 0
## 95 2020-03-06 London 1
## 96 2020-03-07 London 1
## 97 2020-03-08 London 0
## 98 2020-03-09 London 1
## 99 2020-03-10 London 0
## 100 2020-03-11 London 7
## 101 2020-03-12 London 6
## 102 2020-03-13 London 10
## 103 2020-03-14 London 14
## 104 2020-03-15 London 10
## 105 2020-03-16 London 17
## 106 2020-03-17 London 25
## 107 2020-03-18 London 31
## 108 2020-03-19 London 25
## 109 2020-03-20 London 45
## 110 2020-03-21 London 50
## 111 2020-03-22 London 54
## 112 2020-03-23 London 63
## 113 2020-03-24 London 86
## 114 2020-03-25 London 112
## 115 2020-03-26 London 130
## 116 2020-03-27 London 130
## 117 2020-03-28 London 122
## 118 2020-03-29 London 147
## 119 2020-03-30 London 149
## 120 2020-03-31 London 180
## 121 2020-04-01 London 201
## 122 2020-04-02 London 189
## 123 2020-04-03 London 196
## 124 2020-04-04 London 229
## 125 2020-04-05 London 194
## 126 2020-04-06 London 198
## 127 2020-04-07 London 219
## 128 2020-04-08 London 236
## 129 2020-04-09 London 202
## 130 2020-04-10 London 168
## 131 2020-04-11 London 175
## 132 2020-04-12 London 156
## 133 2020-04-13 London 165
## 134 2020-04-14 London 142
## 135 2020-04-15 London 142
## 136 2020-04-16 London 138
## 137 2020-04-17 London 99
## 138 2020-04-18 London 101
## 139 2020-04-19 London 102
## 140 2020-04-20 London 94
## 141 2020-04-21 London 93
## 142 2020-04-22 London 108
## 143 2020-04-23 London 77
## 144 2020-04-24 London 71
## 145 2020-04-25 London 57
## 146 2020-04-26 London 53
## 147 2020-04-27 London 51
## 148 2020-04-28 London 43
## 149 2020-04-29 London 44
## 150 2020-04-30 London 39
## 151 2020-05-01 London 41
## 152 2020-05-02 London 40
## 153 2020-05-03 London 35
## 154 2020-05-04 London 29
## 155 2020-05-05 London 25
## 156 2020-05-06 London 35
## 157 2020-05-07 London 35
## 158 2020-05-08 London 29
## 159 2020-05-09 London 22
## 160 2020-05-10 London 25
## 161 2020-05-11 London 16
## 162 2020-05-12 London 17
## 163 2020-05-13 London 16
## 164 2020-05-14 London 20
## 165 2020-05-15 London 18
## 166 2020-05-16 London 14
## 167 2020-05-17 London 15
## 168 2020-05-18 London 9
## 169 2020-05-19 London 13
## 170 2020-05-20 London 19
## 171 2020-05-21 London 12
## 172 2020-05-22 London 10
## 173 2020-05-23 London 5
## 174 2020-05-24 London 7
## 175 2020-05-25 London 7
## 176 2020-05-26 London 11
## 177 2020-05-27 London 7
## 178 2020-05-28 London 2
## 179 2020-03-01 Midlands 0
## 180 2020-03-02 Midlands 0
## 181 2020-03-03 Midlands 1
## 182 2020-03-04 Midlands 0
## 183 2020-03-05 Midlands 0
## 184 2020-03-06 Midlands 0
## 185 2020-03-07 Midlands 0
## 186 2020-03-08 Midlands 3
## 187 2020-03-09 Midlands 1
## 188 2020-03-10 Midlands 0
## 189 2020-03-11 Midlands 2
## 190 2020-03-12 Midlands 6
## 191 2020-03-13 Midlands 5
## 192 2020-03-14 Midlands 4
## 193 2020-03-15 Midlands 5
## 194 2020-03-16 Midlands 11
## 195 2020-03-17 Midlands 8
## 196 2020-03-18 Midlands 13
## 197 2020-03-19 Midlands 8
## 198 2020-03-20 Midlands 28
## 199 2020-03-21 Midlands 13
## 200 2020-03-22 Midlands 31
## 201 2020-03-23 Midlands 33
## 202 2020-03-24 Midlands 41
## 203 2020-03-25 Midlands 48
## 204 2020-03-26 Midlands 64
## 205 2020-03-27 Midlands 72
## 206 2020-03-28 Midlands 89
## 207 2020-03-29 Midlands 92
## 208 2020-03-30 Midlands 90
## 209 2020-03-31 Midlands 123
## 210 2020-04-01 Midlands 140
## 211 2020-04-02 Midlands 142
## 212 2020-04-03 Midlands 124
## 213 2020-04-04 Midlands 150
## 214 2020-04-05 Midlands 164
## 215 2020-04-06 Midlands 140
## 216 2020-04-07 Midlands 123
## 217 2020-04-08 Midlands 185
## 218 2020-04-09 Midlands 138
## 219 2020-04-10 Midlands 127
## 220 2020-04-11 Midlands 142
## 221 2020-04-12 Midlands 138
## 222 2020-04-13 Midlands 120
## 223 2020-04-14 Midlands 116
## 224 2020-04-15 Midlands 147
## 225 2020-04-16 Midlands 101
## 226 2020-04-17 Midlands 118
## 227 2020-04-18 Midlands 115
## 228 2020-04-19 Midlands 91
## 229 2020-04-20 Midlands 107
## 230 2020-04-21 Midlands 86
## 231 2020-04-22 Midlands 77
## 232 2020-04-23 Midlands 102
## 233 2020-04-24 Midlands 79
## 234 2020-04-25 Midlands 72
## 235 2020-04-26 Midlands 81
## 236 2020-04-27 Midlands 74
## 237 2020-04-28 Midlands 68
## 238 2020-04-29 Midlands 53
## 239 2020-04-30 Midlands 55
## 240 2020-05-01 Midlands 64
## 241 2020-05-02 Midlands 51
## 242 2020-05-03 Midlands 52
## 243 2020-05-04 Midlands 61
## 244 2020-05-05 Midlands 58
## 245 2020-05-06 Midlands 57
## 246 2020-05-07 Midlands 48
## 247 2020-05-08 Midlands 34
## 248 2020-05-09 Midlands 37
## 249 2020-05-10 Midlands 41
## 250 2020-05-11 Midlands 32
## 251 2020-05-12 Midlands 45
## 252 2020-05-13 Midlands 38
## 253 2020-05-14 Midlands 33
## 254 2020-05-15 Midlands 39
## 255 2020-05-16 Midlands 34
## 256 2020-05-17 Midlands 30
## 257 2020-05-18 Midlands 33
## 258 2020-05-19 Midlands 32
## 259 2020-05-20 Midlands 36
## 260 2020-05-21 Midlands 31
## 261 2020-05-22 Midlands 26
## 262 2020-05-23 Midlands 29
## 263 2020-05-24 Midlands 17
## 264 2020-05-25 Midlands 24
## 265 2020-05-26 Midlands 25
## 266 2020-05-27 Midlands 24
## 267 2020-05-28 Midlands 7
## 268 2020-03-01 North East and Yorkshire 0
## 269 2020-03-02 North East and Yorkshire 0
## 270 2020-03-03 North East and Yorkshire 0
## 271 2020-03-04 North East and Yorkshire 0
## 272 2020-03-05 North East and Yorkshire 0
## 273 2020-03-06 North East and Yorkshire 0
## 274 2020-03-07 North East and Yorkshire 0
## 275 2020-03-08 North East and Yorkshire 0
## 276 2020-03-09 North East and Yorkshire 0
## 277 2020-03-10 North East and Yorkshire 0
## 278 2020-03-11 North East and Yorkshire 0
## 279 2020-03-12 North East and Yorkshire 0
## 280 2020-03-13 North East and Yorkshire 0
## 281 2020-03-14 North East and Yorkshire 0
## 282 2020-03-15 North East and Yorkshire 2
## 283 2020-03-16 North East and Yorkshire 3
## 284 2020-03-17 North East and Yorkshire 1
## 285 2020-03-18 North East and Yorkshire 2
## 286 2020-03-19 North East and Yorkshire 6
## 287 2020-03-20 North East and Yorkshire 5
## 288 2020-03-21 North East and Yorkshire 6
## 289 2020-03-22 North East and Yorkshire 7
## 290 2020-03-23 North East and Yorkshire 9
## 291 2020-03-24 North East and Yorkshire 7
## 292 2020-03-25 North East and Yorkshire 18
## 293 2020-03-26 North East and Yorkshire 21
## 294 2020-03-27 North East and Yorkshire 28
## 295 2020-03-28 North East and Yorkshire 35
## 296 2020-03-29 North East and Yorkshire 38
## 297 2020-03-30 North East and Yorkshire 64
## 298 2020-03-31 North East and Yorkshire 60
## 299 2020-04-01 North East and Yorkshire 67
## 300 2020-04-02 North East and Yorkshire 74
## 301 2020-04-03 North East and Yorkshire 99
## 302 2020-04-04 North East and Yorkshire 104
## 303 2020-04-05 North East and Yorkshire 92
## 304 2020-04-06 North East and Yorkshire 95
## 305 2020-04-07 North East and Yorkshire 102
## 306 2020-04-08 North East and Yorkshire 107
## 307 2020-04-09 North East and Yorkshire 111
## 308 2020-04-10 North East and Yorkshire 117
## 309 2020-04-11 North East and Yorkshire 98
## 310 2020-04-12 North East and Yorkshire 84
## 311 2020-04-13 North East and Yorkshire 94
## 312 2020-04-14 North East and Yorkshire 107
## 313 2020-04-15 North East and Yorkshire 95
## 314 2020-04-16 North East and Yorkshire 103
## 315 2020-04-17 North East and Yorkshire 86
## 316 2020-04-18 North East and Yorkshire 95
## 317 2020-04-19 North East and Yorkshire 87
## 318 2020-04-20 North East and Yorkshire 100
## 319 2020-04-21 North East and Yorkshire 76
## 320 2020-04-22 North East and Yorkshire 83
## 321 2020-04-23 North East and Yorkshire 62
## 322 2020-04-24 North East and Yorkshire 72
## 323 2020-04-25 North East and Yorkshire 68
## 324 2020-04-26 North East and Yorkshire 63
## 325 2020-04-27 North East and Yorkshire 65
## 326 2020-04-28 North East and Yorkshire 57
## 327 2020-04-29 North East and Yorkshire 69
## 328 2020-04-30 North East and Yorkshire 56
## 329 2020-05-01 North East and Yorkshire 64
## 330 2020-05-02 North East and Yorkshire 48
## 331 2020-05-03 North East and Yorkshire 39
## 332 2020-05-04 North East and Yorkshire 48
## 333 2020-05-05 North East and Yorkshire 40
## 334 2020-05-06 North East and Yorkshire 50
## 335 2020-05-07 North East and Yorkshire 41
## 336 2020-05-08 North East and Yorkshire 38
## 337 2020-05-09 North East and Yorkshire 43
## 338 2020-05-10 North East and Yorkshire 39
## 339 2020-05-11 North East and Yorkshire 28
## 340 2020-05-12 North East and Yorkshire 25
## 341 2020-05-13 North East and Yorkshire 27
## 342 2020-05-14 North East and Yorkshire 28
## 343 2020-05-15 North East and Yorkshire 30
## 344 2020-05-16 North East and Yorkshire 35
## 345 2020-05-17 North East and Yorkshire 26
## 346 2020-05-18 North East and Yorkshire 26
## 347 2020-05-19 North East and Yorkshire 27
## 348 2020-05-20 North East and Yorkshire 21
## 349 2020-05-21 North East and Yorkshire 30
## 350 2020-05-22 North East and Yorkshire 22
## 351 2020-05-23 North East and Yorkshire 17
## 352 2020-05-24 North East and Yorkshire 22
## 353 2020-05-25 North East and Yorkshire 20
## 354 2020-05-26 North East and Yorkshire 20
## 355 2020-05-27 North East and Yorkshire 15
## 356 2020-05-28 North East and Yorkshire 10
## 357 2020-03-01 North West 0
## 358 2020-03-02 North West 0
## 359 2020-03-03 North West 0
## 360 2020-03-04 North West 0
## 361 2020-03-05 North West 1
## 362 2020-03-06 North West 0
## 363 2020-03-07 North West 0
## 364 2020-03-08 North West 1
## 365 2020-03-09 North West 0
## 366 2020-03-10 North West 0
## 367 2020-03-11 North West 0
## 368 2020-03-12 North West 2
## 369 2020-03-13 North West 3
## 370 2020-03-14 North West 1
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## 372 2020-03-16 North West 2
## 373 2020-03-17 North West 4
## 374 2020-03-18 North West 6
## 375 2020-03-19 North West 6
## 376 2020-03-20 North West 10
## 377 2020-03-21 North West 11
## 378 2020-03-22 North West 13
## 379 2020-03-23 North West 15
## 380 2020-03-24 North West 21
## 381 2020-03-25 North West 20
## 382 2020-03-26 North West 29
## 383 2020-03-27 North West 35
## 384 2020-03-28 North West 27
## 385 2020-03-29 North West 46
## 386 2020-03-30 North West 66
## 387 2020-03-31 North West 52
## 388 2020-04-01 North West 85
## 389 2020-04-02 North West 95
## 390 2020-04-03 North West 94
## 391 2020-04-04 North West 98
## 392 2020-04-05 North West 102
## 393 2020-04-06 North West 100
## 394 2020-04-07 North West 133
## 395 2020-04-08 North West 125
## 396 2020-04-09 North West 119
## 397 2020-04-10 North West 117
## 398 2020-04-11 North West 137
## 399 2020-04-12 North West 126
## 400 2020-04-13 North West 126
## 401 2020-04-14 North West 131
## 402 2020-04-15 North West 114
## 403 2020-04-16 North West 134
## 404 2020-04-17 North West 97
## 405 2020-04-18 North West 113
## 406 2020-04-19 North West 70
## 407 2020-04-20 North West 82
## 408 2020-04-21 North West 76
## 409 2020-04-22 North West 83
## 410 2020-04-23 North West 85
## 411 2020-04-24 North West 65
## 412 2020-04-25 North West 65
## 413 2020-04-26 North West 54
## 414 2020-04-27 North West 54
## 415 2020-04-28 North West 56
## 416 2020-04-29 North West 62
## 417 2020-04-30 North West 59
## 418 2020-05-01 North West 43
## 419 2020-05-02 North West 55
## 420 2020-05-03 North West 55
## 421 2020-05-04 North West 44
## 422 2020-05-05 North West 47
## 423 2020-05-06 North West 41
## 424 2020-05-07 North West 45
## 425 2020-05-08 North West 41
## 426 2020-05-09 North West 28
## 427 2020-05-10 North West 38
## 428 2020-05-11 North West 32
## 429 2020-05-12 North West 36
## 430 2020-05-13 North West 24
## 431 2020-05-14 North West 26
## 432 2020-05-15 North West 33
## 433 2020-05-16 North West 30
## 434 2020-05-17 North West 23
## 435 2020-05-18 North West 28
## 436 2020-05-19 North West 33
## 437 2020-05-20 North West 23
## 438 2020-05-21 North West 23
## 439 2020-05-22 North West 24
## 440 2020-05-23 North West 28
## 441 2020-05-24 North West 24
## 442 2020-05-25 North West 28
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## 466 2020-03-21 South East 7
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## 470 2020-03-25 South East 28
## 471 2020-03-26 South East 34
## 472 2020-03-27 South East 34
## 473 2020-03-28 South East 36
## 474 2020-03-29 South East 54
## 475 2020-03-30 South East 58
## 476 2020-03-31 South East 65
## 477 2020-04-01 South East 65
## 478 2020-04-02 South East 55
## 479 2020-04-03 South East 72
## 480 2020-04-04 South East 80
## 481 2020-04-05 South East 81
## 482 2020-04-06 South East 88
## 483 2020-04-07 South East 99
## 484 2020-04-08 South East 82
## 485 2020-04-09 South East 104
## 486 2020-04-10 South East 88
## 487 2020-04-11 South East 87
## 488 2020-04-12 South East 88
## 489 2020-04-13 South East 83
## 490 2020-04-14 South East 65
## 491 2020-04-15 South East 72
## 492 2020-04-16 South East 56
## 493 2020-04-17 South East 86
## 494 2020-04-18 South East 57
## 495 2020-04-19 South East 69
## 496 2020-04-20 South East 85
## 497 2020-04-21 South East 49
## 498 2020-04-22 South East 54
## 499 2020-04-23 South East 57
## 500 2020-04-24 South East 64
## 501 2020-04-25 South East 50
## 502 2020-04-26 South East 51
## 503 2020-04-27 South East 40
## 504 2020-04-28 South East 40
## 505 2020-04-29 South East 46
## 506 2020-04-30 South East 29
## 507 2020-05-01 South East 37
## 508 2020-05-02 South East 35
## 509 2020-05-03 South East 17
## 510 2020-05-04 South East 35
## 511 2020-05-05 South East 29
## 512 2020-05-06 South East 23
## 513 2020-05-07 South East 25
## 514 2020-05-08 South East 25
## 515 2020-05-09 South East 28
## 516 2020-05-10 South East 19
## 517 2020-05-11 South East 23
## 518 2020-05-12 South East 26
## 519 2020-05-13 South East 18
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## 521 2020-05-15 South East 23
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## 524 2020-05-18 South East 17
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## 531 2020-05-25 South East 12
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## 533 2020-05-27 South East 10
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## 536 2020-03-02 South West 0
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## 538 2020-03-04 South West 0
## 539 2020-03-05 South West 0
## 540 2020-03-06 South West 0
## 541 2020-03-07 South West 0
## 542 2020-03-08 South West 0
## 543 2020-03-09 South West 0
## 544 2020-03-10 South West 0
## 545 2020-03-11 South West 1
## 546 2020-03-12 South West 0
## 547 2020-03-13 South West 0
## 548 2020-03-14 South West 1
## 549 2020-03-15 South West 0
## 550 2020-03-16 South West 0
## 551 2020-03-17 South West 2
## 552 2020-03-18 South West 2
## 553 2020-03-19 South West 5
## 554 2020-03-20 South West 3
## 555 2020-03-21 South West 6
## 556 2020-03-22 South West 9
## 557 2020-03-23 South West 9
## 558 2020-03-24 South West 7
## 559 2020-03-25 South West 9
## 560 2020-03-26 South West 11
## 561 2020-03-27 South West 13
## 562 2020-03-28 South West 21
## 563 2020-03-29 South West 18
## 564 2020-03-30 South West 23
## 565 2020-03-31 South West 23
## 566 2020-04-01 South West 22
## 567 2020-04-02 South West 23
## 568 2020-04-03 South West 30
## 569 2020-04-04 South West 42
## 570 2020-04-05 South West 32
## 571 2020-04-06 South West 34
## 572 2020-04-07 South West 39
## 573 2020-04-08 South West 47
## 574 2020-04-09 South West 24
## 575 2020-04-10 South West 46
## 576 2020-04-11 South West 43
## 577 2020-04-12 South West 23
## 578 2020-04-13 South West 26
## 579 2020-04-14 South West 24
## 580 2020-04-15 South West 31
## 581 2020-04-16 South West 29
## 582 2020-04-17 South West 33
## 583 2020-04-18 South West 25
## 584 2020-04-19 South West 31
## 585 2020-04-20 South West 26
## 586 2020-04-21 South West 26
## 587 2020-04-22 South West 22
## 588 2020-04-23 South West 17
## 589 2020-04-24 South West 19
## 590 2020-04-25 South West 15
## 591 2020-04-26 South West 27
## 592 2020-04-27 South West 13
## 593 2020-04-28 South West 17
## 594 2020-04-29 South West 14
## 595 2020-04-30 South West 26
## 596 2020-05-01 South West 6
## 597 2020-05-02 South West 7
## 598 2020-05-03 South West 10
## 599 2020-05-04 South West 16
## 600 2020-05-05 South West 14
## 601 2020-05-06 South West 18
## 602 2020-05-07 South West 16
## 603 2020-05-08 South West 5
## 604 2020-05-09 South West 10
## 605 2020-05-10 South West 5
## 606 2020-05-11 South West 7
## 607 2020-05-12 South West 7
## 608 2020-05-13 South West 7
## 609 2020-05-14 South West 6
## 610 2020-05-15 South West 3
## 611 2020-05-16 South West 4
## 612 2020-05-17 South West 6
## 613 2020-05-18 South West 4
## 614 2020-05-19 South West 6
## 615 2020-05-20 South West 1
## 616 2020-05-21 South West 9
## 617 2020-05-22 South West 6
## 618 2020-05-23 South West 6
## 619 2020-05-24 South West 3
## 620 2020-05-25 South West 7
## 621 2020-05-26 South West 10
## 622 2020-05-27 South West 5
## 623 2020-05-28 South West 11.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Thursday 28 May 2020.
1.6 Add variables
We add the following variable:
day: an integer representing the number of days from the earliest data reported, used for modelling purposes; the first day is 0
1.7 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 8,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 6,
lab_pos_y = 30000,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 16 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 16 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.7028 -2.5398 0.0328 2.0587 7.3570
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.573e+00 5.485e-02 101.61 <2e-16 ***
## note_lag 8.147e-06 5.341e-07 15.25 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 10.5202)
##
## Null deviance: 2792.45 on 34 degrees of freedom
## Residual deviance: 345.99 on 33 degrees of freedom
## (16 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 263.284469 1.000008
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 236.201540 292.862829
## note_lag 1.000007 1.000009
Rsq(lag_mod)
## [1] 0.8760989
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.4
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.3.0 lubridate_1.7.8
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.13
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.1.1
## [10] projections_0.4.1 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.0 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.0 tibble_3.0.1 ggplot2_3.3.1
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 selectr_0.4-2 ggsignif_0.6.0 ellipsis_0.3.1
## [5] rprojroot_1.3-2 snakecase_0.11.0 fs_1.4.1 rstudioapi_0.11
## [9] farver_2.0.3 fansi_0.4.1 splines_3.6.3 knitr_1.28
## [13] jsonlite_1.6.1 broom_0.5.6 dbplyr_1.4.4 compiler_3.6.3
## [17] httr_1.4.1 backports_1.1.7 assertthat_0.2.1 Matrix_1.2-18
## [21] cli_2.0.2 htmltools_0.4.0 prettyunits_1.1.1 tools_3.6.3
## [25] gtable_0.3.0 glue_1.4.1 Rcpp_1.0.4.6 carData_3.0-4
## [29] cellranger_1.1.0 vctrs_0.3.0 nlme_3.1-144 matchmaker_0.1.1
## [33] crosstalk_1.1.0.1 xfun_0.14 ps_1.3.3 openxlsx_4.1.5
## [37] lifecycle_0.2.0 rstatix_0.5.0 MASS_7.3-51.5 scales_1.1.1
## [41] hms_0.5.3 sodium_1.1 yaml_2.2.1 curl_4.3
## [45] gridExtra_2.3 stringi_1.4.6 kyotil_2019.11-22 boot_1.3-24
## [49] pkgbuild_1.0.8 zip_2.0.4 rlang_0.4.6 pkgconfig_2.0.3
## [53] evaluate_0.14 lattice_0.20-38 labeling_0.3 htmlwidgets_1.5.1
## [57] cowplot_1.0.0 processx_3.4.2 tidyselect_1.1.0 plyr_1.8.6
## [61] magrittr_1.5 R6_2.4.1 generics_0.0.2 DBI_1.1.0
## [65] pillar_1.4.4 haven_2.3.0 foreign_0.8-75 withr_2.2.0
## [69] mgcv_1.8-31 survival_3.1-8 abind_1.4-5 modelr_0.1.8
## [73] crayon_1.3.4 car_3.0-8 utf8_1.1.4 rmarkdown_2.1
## [77] viridis_0.5.1 grid_3.6.3 readxl_1.3.1 data.table_1.12.8
## [81] blob_1.2.1 callr_3.4.3 reprex_0.3.0 digest_0.6.25
## [85] webshot_0.5.2 munsell_0.5.0 viridisLite_0.3.0